If equation of ellipse is `(3x-9)^2+9y^2=(x+sqrt(2)y+1)^2` then (1) Its eccentricity is `1/(sqrt(3))` (2) Its eccentricity is `1/(sqrt(2))` (3) Length of major axis is 4' (4) Length of minor axis is 4'

For equation of the curve whose subnormal is constant, then (a) its eccentricity is 1 (b) its eccentricity is sqrt(2) (c) its axis is the x-axis (d)its axis is the y-axis.

Find the equation of the ellipse whose centre is the origin, major axis 9/2 and eccentricity 1/sqrt(3) where the major axis is the horizontal axis.

Find the equation to the ellipse whose one focus is (2, 1), the directrix is 2x-y+3=0 and the eccentricity is 1/sqrt(2)

Find the equation to the ellipse whose one focus is (2, 1) , the directrix is 2x-y+3=0 and the eccentricity is 1/sqrt(2) .

Find the equation of the ellipse whose : One focus is (6, 7) , directrix is x + y + 2 and eccentricity is 1/sqrt(3)

If the minor axis of an ellipse is equal to the distance between its foci, prove that its eccentricity is 1/sqrt(2) .

The eccentricity of ellipse 4(x-2y+1)^2 +9(2x+y+2)^2=180 is

If the latus rectum of an ellipse is equal to half of minor axis, then its eccentricity is (i) sqrt((3)/(2)) (ii) (sqrt(3))/(2) (iii) (1)/(2) (iv) None of these

For the ellipse x^2+4y^2=9 a. the eccentricity is 1/2 b. the latus rectum is 3/2 c. a focus is (3sqrt(3),0) d. a directrix is x=-2sqrt(3)

Consider two straight lines, each of which is tangent to both the circle x^2+y^2=1/2 and the parabola y^2=4x . Let these lines intersect at the point Q . Consider the ellipse whose center is at the origin O(0,\ 0) and whose semi-major axis is O Q . If the length of the minor axis of this ellipse is sqrt(2) , then which of the following statement(s) is (are) TRUE? For the ellipse, the eccentricity is 1/(sqrt(2)) and the length of the latus rectum is 1 (b) For the ellipse, the eccentricity is 1/2 and the length of the latus rectum is 1/2 (c) The area of the region bounded by the ellipse between the lines x=1/(sqrt(2)) and x=1 is 1/(4sqrt(2))(pi-2) (d) The area of the region bounded by the ellipse between the lines x=1/(sqrt(2)) and x=1 is 1/(16)(pi-2)